Using shortcodes in input type text fields

I do not think so. What are you trying to achieve? Maybe there is a different way.

I want to get a phone number of the logged in user. I saw that there are some predefined variables like {CurUserName}, can I define some custom ones ?

No you cannot up to now, but maybe there will be a way in the future. Please also see https://www.ads-software.com/support/topic/own-variables.

I think this may be what I’m look for also.

I’d like to put a shortcode for another plugin into a field.

In my case it would be [catlist id=10] which would list all posts in a given category. Put that list in a select box or radio buttons. That might be a tall ask.